Note: Each problem begins with a list of forces
necessary to solve the context-rich problem. These are for the
benefit of the instructor. Delete the list before using the
problems in your class.

Weight, Normal: Just before finals you decide to visit an
amusement park set up in the Metrodome. Since it is a
weekend, you invite your favorite niece along. She loves
to ride on a Ferris wheel, and there is one at the
amusement park. The Ferris wheel has seats on the rim of
a circle with a radius of 25 m. The Ferris wheel rotates
at a constant speed and makes one complete revolution
every 20 seconds. While you wait, your niece who has a
mass of 42 kg, rides the Ferris wheel. To kill time you
decide to calculate the total force (both magnitude and
direction) on her when she is one quarter revolution past
the highest point. Because the Ferris wheel can be run at
different speeds, you also decide to make a graph which
gives the magnitude of the force on her at that point as
a function of the period of the Ferris wheel.

Weight, Normal: While watching TV, you see a circus show
in which a performer drives a motorcycle around the inside of a vertical
ring. You wonder how far the cycle would fall if the rider made a
mistake at the top of the loop and fell off the track and decide to
calculate it. You determine that the cycle is going around at a constant
speed and that it takes at most 4.0 seconds to get around the ring. At
this speed, the motorcycle just barely loses contact with the ring at
the top when it is upside down and is in free fall.

Weight, Normal, Friction: The producer of the last film
you worked on was so impressed with the way you handled a
helicopter scene that she hired you again as technical
advisor for a new "James Bond" film. The scene
calls for 007 to chase a villain onto a merry-go-round.
An accomplice starts the merry-go-round rotating in an
effort to toss 007 (played in this new version by Billy
Crystal) off into an adjacent pool filled with hungry
sharks. You must determine a safe rate of rotation such
that the stunt man (you didn't think Billy would do his
own stunts did you?) will not fly off the merry-go-round
and into the shark-infested pool. (Actually they are
mechanical sharks, but the audience doesn't know that.)
You measure the diameter of the merry-go-round as 50
meters. You determine that the coefficient of static
friction between 007's shoes and the merry-go-round
surface is 0.7 and the coefficient of kinetic friction is
0.5.

Weight, Normal, Friction: A new package moving
system in the new, improved post office consists of a
large circular disc (i.e. a turntable) which rotates once
every 3.0 seconds at a constant speed in the horizontal
plane. Packages are put on the outer edge of the
turntable on one side of the room and taken off on the
opposite side. The coefficient of static friction between
the disc surface and a package is 0.80 while the
coefficient of kinetic friction is 0.60. If this system
is to work, what is the maximum possible radius of the
turntable?

Weight, Normal, Friction: You are driving with a friend
who is sitting to your right on the passenger side of the
front seat. You would like to be closer to your friend
and decide to use your knowledge of physics to achieve
your romantic goal. So you'll make a sharp turn. Which
direction should you turn so as to make your friend slide
closer to you? If the coefficient of static friction
between your friend and the seat of the car is 0.40, and
you drive at a constant speed of 18 m/s, what is the
maximum radius you could make your turn and still have
your friend slide your way?

Weight, Normal, Friction: During a freeway safety review, you
are studying a piece of one road with a curve that is essentially 1/8 of
a circle with a radius of 0.5 miles. The curve is banked so that the
road makes an angle of 4 degrees to the horizontal throughout the curve.
Your boss asks you to help determine the speed limit for a standard
passenger car (about 2000 lbs) to complete the turn. You decide to start
by considering the worst-case scenario, a slick, ice-covered road, and
finding the constant speed a car must travel in order to maintain a
horizontal path through the turn.

Weight, Tension: After watching the movie "Crocodile
Dundee," you and some friends decide to make a
communications device invented by the Australian
Aborigines. It consists of a noise-maker swung in a
vertical circle on the end of a string. Your design calls
for a 400 gram noise-maker on a 60 cm string. You are
worried about whether the string you have will be strong
enough, so you decide to calculate the tension in the
string when the device is swung with an acceleration
which has a constant magnitude of 20 m/s2 . You and your
friends can't agree whether the maximum tension will
occur when the noise maker is at the highest point in the
circle, at the lowest point in the circle, or is always
the same. To settle the argument you decide to calculate
the tension at the highest point and at the lowest point
and compare them.

You are watching a TV news program when they switch to
some scenes taken aboard the space shuttle which circles
500 miles above the Earth once every 95 minutes. To allow
the audience to appreciate the distances involved, the
announcer tells you that the radius of the Earth is about
4000 miles and the distance from the Earth to the Moon is
about 250,000 miles. When an astronaut drops her pen it
floats in front of her face. You immediately wonder how
the acceleration of the dropped pen compares to the
acceleration of a pen that you might drop here on the
surface of the Earth.

Gravitational: You are still a consultant for the new
Star Trek TV series. You were hired to make sure that any
science on the show is correct. In this episode, the crew
of the Enterprise discovers an abandoned space station in
deep space far from any stars. This station, which was
built by Earth in the 21st century, is a large wheel-like
structure where people live and work in the rim. In order
to create "artificial gravity," the space
station rotates on its axis. The special effects
department wants to know at what rate a space station 200
meters in diameter would have to rotate to create
"gravity" equal to 0.7 that of Earth.

Gravitational: You did so well in your physics course
that you decided to try to get a summer job working in a
physics laboratory at the University. You got the job as
a student lab assistant in a research group investigating
the ozone depletion at the Earth's poles. This group is
planning to put an atmospheric measuring device in a
satellite which will pass over both poles. To collect
samples of the upper atmosphere, the satellite will be in
a circular orbit 200 miles above the surface of the
Earth. To adjust the instruments for the proper data
taking rate, you need to calculate how many times per day
the device will sample the atmosphere over the South
pole. Using the inside cover of your trusty Physics text
you find that the radius of the Earth is 6.38 x 103 km,
the mass of the Earth is 5.98 x 1024 kg, and the
universal gravitational constant is 6.7 x 10-11 N m2/kg2.

Gravitational: You did so well in your physics course
that you decided to try to get a summer job working in a
physics laboratory at the University. You got the job as
a student lab assistant in a research group investigating
the ozone depletion at the Earth's poles. This group is
planning to put an atmospheric measuring device in a
satellite which will pass over both poles. To collect
samples of the upper atmosphere, the satellite will be in
a circular orbit 200 miles above the surface of the Earth
where g is 95% of its value on the Earth's surface. To
adjust the instruments for the proper data taking rate,
you need to calculate how many times per day the device
will sample the atmosphere over the South pole. Using the
inside cover of your trusty Physics text you find that
the radius of the Earth is 6.38 x 103 km and the mass of
the Earth is 5.98 x 1024 kg.

Gravitational: You are reading a magazine article about
pulsars. A few years ago, a satellite in orbit around the
Earth detected X-rays coming from sources in outer space.
The X-rays detected from one source, called Cygnus X-3,
had an intensity which changed with a period of 4.8
hours. This type of astronomical object emitting periodic
signals is called a pulsar. One popular theory holds that
the pulsar is a normal star (similar to our Sun) which is
in orbit around a much more massive neutron star. The
period of the X-ray signal is then the period of the
orbit. In this theory, the distance between the normal
star and the neutron star is approximately the same as
the distance between the Earth and our Sun. You realize
that if this theory is correct, you can determine how
much more massive the neutron star is than our Sun. All
you need to do is first find the mass of the neutron star
in terms of two unknowns, the universal gravitational
constant G and the radius of the Earth's orbit. Then find
the mass of our Sun in terms of the same two unknowns, G
and the radius of the Earth's orbit. (The period of the
Earth's orbit is 1 year). Then you can calculate how many
times more massive the neutron star is than our Sun.

Note: Each problem begins with a list of forces
necessary to solve the context-rich problem. These are for the
benefit of the instructor. Delete the list before using the
problems in your class.

Weight, Lift: You are reading an article about the
aesthetics of airplane design. One example in the article
is a beautiful new design for commercial airliners. You
are worried that this light wing structure might not be
strong enough to be safe. The article explains that an
airplane can fly because the air exerts a force, called
"lift," on the wings such that the lift is
always perpendicular to the wing surface. For level
flying, the wings are horizontal. To turn , the pilot
"banks" the plane so that the wings are
oriented at an angle to the horizontal. This causes the
plane to have a trajectory which is a horizontal circle.
The specifications of the 100 x 103 lb plane require that
it be able to turn with a radius of 2.0 miles at a
constant speed of 500 miles/hr. The article states that
tests show that the new wing structure will support a
force 4 times the lift necessary for level flight. Is the
wing structure sufficiently strong for the plane to make
this turn?

Weight, Lift: You are flying to Chicago when the pilot
tells you that the plane can not land immediately because
of airport delays and will have to circle the airport.
This is standard operating procedure. She also tells you
that the plane will maintain a speed of 400 mph at an
altitude of 20,000 feet while traveling in a horizontal
circle around the airport. To pass the time you decide to
figure out how far you are from the airport. You notice
that to circle, the pilot "banks" the plane so
that the wings are oriented at 10o to the horizontal. An
article in your in-flight magazine explains that an
airplane can fly because the air exerts a force, called
"lift," on the wings. The lift is always
perpendicular to the wing surface. The magazine article
gives the weight of the type of plane you are on as 100 x
103 pounds and the length of each wing as 150 feet. It
gives no information on the thrust of the engines or the
drag of the airframe.

Because of your physics background, you have been hired
as a member of the team the state highway department has
assigned to review the safety of Minnesota freeways. This
week you are studying 35W which has a curve which is
essentially 1/8 of a circle with a radius of 0.5 miles.
The road has been designed with a banked curve so that
the road makes an angle of 4û to the horizontal
throughout the curve. To begin the study, the head of
your department asks that you calculate the maximum speed
for a standard passenger car (about 2000 lbs) to complete
the turn while maintaining a horizontal path along the
road. She asks that you first consider the case of a
slick, ice covered road. When you have completed that
calculation she wants you to do the case of a dry, clear
road where the coefficient of kinetic friction is 0.70
and the coefficient of static friction is 0.80 between
the tires and the road. This will give her team the two
extremes of Minnesota driving conditions on which to base
the analysis.

Tension, Weight: A neighbor's child wants to go to a
neighborhood carnival to experience the wild rides. The
neighbor is worried about safety because one of the rides
looks dangerous. She knows that you have taken physics
and so asks your advice. The ride in question has a 10-lb
chair which hangs freely from a 30-ft long chain attached
to a pivot on the top of a tall tower. When a child
enters the ride, the chain is hanging straight down. The
child is then attached to the chair with a seat belt and
shoulder harness. When the ride starts up the chain
rotates about the tower. Soon the chain reaches its
maximum speed and remains rotating at that speed. It
rotates about the tower once every 3.0 seconds. When you
ask the operator, he says that the ride is perfectly
safe. He demonstrates this by sitting in the stationary
chair. The chain creaks but holds and he weighs 200 lbs.
Has the operator shown that this ride safe for a 50-lb
child?